Two coil guidance system for tracking boreholes

ABSTRACT

A method and apparatus for tracking the drilling progress of a borehole such as a horizontal borehole that is drilled under an obstacle along a prescribed path is based upon triangulation from two laterally separated loops of wire lying on the ground, which generate corresponding alternating magnetic fields.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit under 35 U.S.C. 119(e) of U.S.Provisional Application No. 61/166,443, filed Apr. 3, 2009 and entitled“Two Coil Guidance System for Tracking Boreholes,” the entire disclosureof which is hereby incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to a method and apparatus for tracking andguiding the drilling of a borehole, and more particularly to tracking aborehole being drilled generally horizontally under an obstacle such asa river, a highway, a railroad, an airport runway or the like, whereaccess to the ground above the borehole is difficult or perhaps notpossible. Various well-known drilling techniques have been used in theplacement of underground transmission lines, communication lines,pipelines, or the like through or beneath obstacles of various types. Inorder to traverse the obstacle, the borehole must be tunneled along aplanned path underneath the obstacle from an entry point on the Earth'ssurface to a desired exit point The borehole then may receive a casingwhich may be used, for example, as a pipeline or for receiving cablesfor use as power transmission lines, communication lines, or the like.In the drilling of such boreholes, it is important to maintain them on acarefully controlled track following a prescribed drilling proposal, foroften the borehole must remain within a precisely defined right of wayas it passes under the obstacle and its entry and exit points onopposite sides of the obstacle must often be at precisely definedlocations. In order to do this, the driller must have an accuratedetermination of the lateral position of the borehole as it is beingdrilled, as well as the precise distance to the exit location so thatappropriate adjustments to the inclination and direction of drilling canbe made. Even if the radial distance to the exit location from the entrypoint of the borehole into the Earth is precisely known and the radialdistance of the drill bit from its entry point into the Earth isprecisely known, safety considerations alone give high priority todirectly determining the relative location of the desired borehole exitpoint with respect to the drill bit location as the exit point isapproached.

Conventional directional drilling techniques used to drill suchboreholes commonly use a steering tool which measures the boreholeinclination, azimuth and tool roll angle at each station along the pathwhere measurements are made. The borehole coordinates are computed andtabulated from these steering tool data as a function of the measureddistance along the borehole, which may be referred to as the measureddepth of the steering tool, or the “away” distance from a referencepoint such as the borehole entry point. However, these boreholecoordinates suffer from serious cumulative effects caused by smallerrors in the inclination and azimuth determinations made at regularlyspaced stations along the borehole, and the lateral errors generated bysuch conventional borehole surveying are intolerable.

A number of prior electromagnetic systems present problems to the usersince they require access to the land directly above the path to befollowed by the borehole in order to permit placement of surface gridsor other guidance systems. Often, however, access to this land is notavailable; furthermore, the placement of guidance systems of this kindcan be extremely time consuming, and thus expensive. The Earth'smagnetic field is usually utilized for determining azimuthal directionin such prior systems, but this creates additional problems because ofthe disturbances caused by nearby steel objects such as bridges,vehicular traffic and trains. Therefore, although steering toolinclinometers provide good inclination measurements, usually to aprecision of 0.1 or 0.2 degrees, the standard steering tool azimuthaldirection determination provided by the Earth Field magnetometers isinadequate.

To avoid the need for placing guide wire grids on the earth's surfaceabove the proposed borehole path, systems have been provided for guidinga drill in which a solenoid generates magnetic field signals that aremeasured at field sensors at the drill stem. One such system isillustrated in U.S. Pat. No. 5,513,710 to Kuckes, which discloses adrilling guidance method for drilling boreholes under rivers and otherobstacles using a direct current powered solenoid and an industrystandard MWD system.

U.S. Pat. Nos. 6,626,252 and 6,814,163, to Kuckes, similarly describe adrill tool which includes a three-axis magnetometer for detecting vectorcomponents of target magnetic fields produced by a large solenoid whichincorporates a coil surrounding a large ferromagnetic core. The solenoidis connected to a reversible source of direct current of sufficientmagnitude to provide a target magnetic field in the region of theproposed path of the drilling.

In systems for guiding horizontal boreholes such as those described inthe '710, the '252 and the '163 patents, the drilling equipment isplaced at a location where a borehole is to be started, while the targetsolenoid is positioned at or near the area where the borehole is to exitthe ground. The borehole entrance may be at or near one side of anobstacle, such as the bank of a river, with the borehole passing beneaththe river to an exit beyond the opposite bank. Drilling the borehole isbegun at the entrance site and conventional survey methods are used toguide the drill for a major part of the distance toward the exitlocation. As the borehole nears the desired exit site; for example,within about 100 meters, further guidance is by way of the targetsolenoid field. Whenever a survey is required, the drill is stopped andthe sensor system in the drilling tool is activated to measure the x, yand z components of the total magnetic field in the region of thesensor. These measurements, together with downhole tool orientationmeasurements, are then used to determine the distance and direction fromthe drilling tool to the solenoid.

Still another prior system is illustrated in U.S. Pat. No. 6,466,020 toKuckes et al, wherein a target magnetic field for borehole drillingguidance is generated by a loop/guide wire antenna system on the Earth'ssurface above the proposed path of the borehole. The loop is energizedby a known current to generate a magnetic field that is measured by twosingle-axis electromagnetic field sensors that lie on an imaginaryspherical surface at the known radial distance from a point such as theentry point of the borehole. These sensors are approximatelyperpendicular to the radius of this spherical segment and to each other.Measurement of the two perpendicular electromagnetic field componentsgenerated by the loop is made by the two sensors at a selected boreholesite. The radial distance from the drill bit entry point to the selectedmeasurement site is determined using standard integration techniques, aswell as steering tool measurements of inclination from the Earth'sgravity and azimuth from the Earth's magnetic field along the boreholetogether with the measured depth of the sensors. The electromagneticfield measurements by these two sensors together with this computedradial distance from the entry point are matched to theoreticallycomputed values for field vectors on the imaginary spherical surface atthe known radial distance of the measurement site to determine thelocation of the drill bit.

A second embodiment of the system described in the '020 patent includestwo electromagnetic field source loops, both near the punch-outlocation. A guide wire leg of each loop is positioned on the Earth'ssurface along the proposed path of the borehole to produce correspondingelectromagnetic fields on that path. The loop geometry is designed sothat there is a rapid variation in the x and y components of the fieldsgenerated near the portion of the borehole beyond the edge of the loops.The rapid variations in the x and y field components in this region areused find the radial distance from the drill bit to the proposed punchout location. The radial distance to the punch out point is usually acritical parameter.

Although such prior systems are useful in various drilling guidanceapplications, it has been found that a continuing problem in horizontaldrilling of boreholes is the accurate determination of the lateralposition of the drill bit in a borehole and the direction of drillingwhen the drill bit is far from the point at which the borehole passesunder an obstacle; for example when it is at a great distance from theshore of a river.

SUMMARY OF THE INVENTION

The present invention is directed to an improved method and apparatusfor providing guidance in drilling boreholes. The invention disclosedherein uses two electromagnetic sources consisting of two laterallyspaced-apart loops of wire carrying alternating current to providetarget magnetic fields that are used to determine the location anddirection of the drill head and to guide further drilling. At least oneof the loops is significantly off to one side of the borehole beingtracked, and preferably both loops are laterally spaced from theproposed path. In one preferred form of the invention, two laterallyspaced loops are on opposite sides of the proposed path and of the exitpoint of the borehole. Vector components of the electromagnetic fieldsare measured near the drill bit in the borehole by an array of magneticfield sensors, and accelerometers are provided to determine thedirection of the Earth's gravitational field at the location of themagnetic field sensors. These electromagnetic field and accelerometermeasurements are analyzed by mathematical techniques using the knownloop geometry and electric currents to determine the drill bit locationand the azimuthal direction of drilling. The drilling inclinationdirection is determined using standard accelerometer data.Alternatively, the location vector to the drilling point can bedetermined from the measured electromagnetic field vectors without theuse of an accelerometer. The detailed geometry, power levels andfrequency of operation and signal averaging time are subject to designcriteria constraints including factors such as the size and location ofthe spaces available for positioning the loops and the consequentdiameters of the loops and the number of turns of wire in each loop.

The method, and the advantages, of the present system are illustrated byselecting an exemplary set of typical parameters for the wire loops usedin the invention. In this example, two source wire loops are provided,one on each side of the borehole path, with each loop beingapproximately 50 meters in diameter and the loops being laterallyseparated by 150 meters. Each loop is powered by 5 kilowatts to generatecorresponding magnetic fields, which may be referred to as targetfields. Measurement of the target magnetic fields generated by thiscurrent at a selected point, such as a field detector on a drill head500 meters distant from the loops, readily provides a lateral locationprecision of 5 meters with respect to the proposed path and a fewdegrees precision in the drilling direction after a short period ofsignal averaging. Measurements made at a drilling location closer to thesource loops will yield more precise results.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and additional objects, features and advantages of thepresent invention will be apparent to those of skill in the art from aconsideration of the following detailed description of a preferredembodiment thereof, taken in conjunction with the accompanying drawings,in which:

FIG. 1 is a diagrammatic illustration of a drill guidance systemutilizing the invention for guiding the drilling of a horizontalborehole following a proposed path to a proposed punch out point, inwhich two electromagnetic guidance coils are deployed on the far side ofan obstacle, illustrated as a river;

FIG. 2 is a diagrammatic top plan view of a portion of the guidancesystem of FIG. 1;

FIG. 3 is a diagrammatic illustration of exemplary downholeinstrumentation and an up hole computer in accordance with theinvention;

FIG. 4 is a diagrammatic illustration of the electronics powering eachof the two loops of the illustrated configuration of FIG. 1;

FIG. 5 is a diagrammatic illustration of the current and clock signalcontrolling each of the loops of the configuration of FIG. 1;

FIG. 6 is a diagrammatic illustration of the wire loop geometry togetherwith representations of the symbols used for the relative positionvectors of a loop and a downhole location P;

FIG. 7 is a diagrammatic illustration showing the representation ofquantities which enter into the theoretical computation of theelectromagnetic field generated by a loop segment at the point P;

FIG. 8 is a diagrammatic representation of the xyz unit vectors and ofthe bes unit vectors together with the direction of gravity; and

FIG. 9 is a top view, looking vertically down showing the relationshipof the a, e, and r unit vectors of the aer coordinate system and of theb, e, and s unit vectors of the bes coordinate system.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

A unique and novel feature of the present application is the utilizationof two independent, laterally separated source loops to generateelectromagnetic fields for use in determining the location and directionof field sensors, and more particularly for guiding borehole drilling.Such laterally displaced source loops give a much greater useful rangeaway from the electromagnetic field source for better distant locationresolution and for more accurately guiding the drilling of a borehole,than has heretofore been possible.

One embodiment of the apparatus utilized in the method of the presentinvention is generally illustrated at 10 in FIG. 1, wherein a borehole12 is drilled under an obstacle such as a river for use in the laying ofpipeline, for example. The apparatus incorporates a drill head having adown-hole industry standard drilling motor 14 for driving a drilling bitunder the control of equipment at a drill rig 16 at the Earth's surface.The crossing of the river 18 may entail drilling along a planned path 20which may pass under the river at a depth of 30 meters, for example, toa planned “punch-out point”, or exit location 22, which may be, forexample, 1000 to 1500 meters away from a borehole entry point 24. Theprogress of the borehole may be tracked for part of the distance to theexit point by conventional survey equipment, but as the drill bit movesfurther away from the entry point 24, guidance of the drill bit is bestcarried out by the use of target magnetic fields generated by two wireloops 26 and 28. In this case the loops are illustrated as being locatedbeyond the far bank 32 of the river 18, on the surface 34 of the Earthat the exit side of the river. It will be understood that the loops maybe located on the near side of the river or other obstacle, or in somecases pairs of loops may be provided on both sides of the obstacle forprecision guidance of the drill. The method is particularly importantfor drilling guidance while drilling under a river or other obstaclewhere it is impractical to deploy a guide wire system on the surface.

The loops 26 and 28 are energized, as will be explained below, toproduce target magnetic fields that are detected at selected measurementstations along the proposed path by a measurement while drilling (MWD)package 36 located on the drill head at or near the drilling motor 14 toprovide the information needed to guide the drilling at each measurementstation under the river and subsequently under the earth's surface 34 asdrilling progresses toward the proposed exit location 22. As illustratedin the embodiment of FIG. 1, the drilling motor 14 is mounted on a drillstem 38 to drive a drill bit 40, in conventional manner. The MWD package36 preferably includes a conventional three component accelerometer tomeasure the direction of gravity and a conventional three componentmagnetometer to measure alternating magnetic fields, and is mounted onthe drill stem adjacent, and just above, the drilling motor.

In the preferred form of the invention, the loop sources 26 and 28 arelaterally spaced from each other, and are positioned by land surveyingtechniques at selected, known locations with respect to the proposedpath 20 of the borehole being drilled. At least one of the loop sourcesis laterally displaced a significant distance from the proposed path 20.Preferably, both loops are displaced from the path. And advantageouslythe loops are on opposite sides of path 20, as illustrated in FIGS. 1and 2. Each loop may consist of 5 turns of #12 wire, and may be 50meters in diameter d. As illustrated in FIG. 2, the centers 50 and 51 ofloops 26 and 28, respectively, are separated by approximately 150meters, and in the illustrated embodiment are equally spaced bydistances 52 and 53 on opposite sides of the path 20, with a linebetween the center points 50 and 51 being perpendicular to the proposedpath 20.

The loops 26 and 28 are energized by a 5 kw motor/generator set 54through suitable power control electronics 56 and power lines 58 and 60,respectively, as diagrammatically illustrated in FIG. 1. The controlelectronics simultaneously supply power to the two loops at differentfrequencies; for example, loop 26 may be energized by an alternatingcurrent having a frequency of 1 Hertz, while loop 28 is energized byalternating current at a frequency of 1.14 Hertz, to producecorresponding magnetic fields in the Earth in the region of the path 20.Alternatively, the loops may be separately energized by AC currents atthe same frequency, in which case two sets of measurements are madesequentially, first with one loop powered and then with the second beingpowered. The important point is that independent measurements are madeof the electromagnetic field components generated by each loop.

In the illustrated embodiment of the invention, the magnetic fieldsource loops 26 and 28 are positioned near the planned punch-out point22 of the borehole, in this case on the far side of the obstacle underwhich the borehole is to be drilled, from the entry point of theborehole. It will be understood, however, that the source loops can bepositioned at any location along, or even beyond, the path 20, whereverprecise lateral control of the drill bit and thus of the direction ofdrilling, is needed. It is to be noted that the larger the lateralseparation of the loops and the fewer the number of turns for a fixedlength of wire and excitation power, the better. The choice ofparameters, in the example given above, is based on the limitationsimposed by land accessibility and other such factors in the region ofthe path 20 of the borehole, and may vary in accordance with specificapplications.

Data Acquisition and Processing

Typically, the direction of drilling a borehole, such as the illustratedborehole 24, is initially controlled by standard borehole surveyingtechniques in which a steering tool measures the borehole inclination,azimuth and tool roll angle at successive stations along the path of theborehole. The borehole coordinates are computed and tabulated from thesteering tool data as a function of the measured distance along theborehole and directional signals are generated and sent to the steeringtool to control further drilling. However, as described above, theseborehole coordinates suffer from serious cumulative effects caused bysmall errors in the inclination and azimuth determinations made atregularly spaced stations along the borehole, and the lateral errorsgenerated by such conventional borehole surveying can cause seriousproblems. In accordance with the present invention, these lateral errorsare overcome by utilizing the magnetic fields generated by laterallyspaced loops 26 and 28 located where lateral drilling precision isneeded.

To obtain the data needed for accurate location of the drill head, whichmay include the drilling motor 14 and the drill bit 40, the loops 26 and28 are electrically excited by alternating current after drilling hasbeen stopped at a measurement station along the proposed borehole path.The resulting alternating electromagnetic fields are detected by thedownhole MWD instrument package 36 on the drill string, and theresulting output data signals are transmitted uphole to the drillingapparatus 16, a few minutes of data are recorded and the data file isgenerated.

As illustrated in FIG. 3, the MWD package 36 incorporates conventionalmagnetometers 60 for measuring the x, y and z vector components of theAC magnetic fields generated by the current flow in the loops 26 and 28and the x, y and z components of the Earth's magnetic field. The ACmagnetometer output signals are supplied through corresponding ACamplifiers 62, and the Earth's magnetic field vector signals aresupplied directly, to respective inputs of multiplexer and telemetrycircuitry 64 which is driven by a suitable downhole clock circuit 66.The MWD package also incorporates x, y and z accelerometers 68 formeasuring the x, y and z components of the Earth's gravity and suppliescorresponding output signals to inputs of multiplexer 64. Themultiplexer output is connected by way of a suitable communications linksuch as a cable 70 to uphole communication equipment 72 which includesan instrument power supply and telemetry circuits 74. Equipment 72 alsoincludes an uphole computer 76 which receives demultiplexed data signalsfrom the telemetry circuitry 74 at Earth's field circuit 76, gravitycircuit 78, and AC field circuit 80. These signals are recorded atcorresponding data files 82, 84 and 86, respectively, and the computerthen determines the direction of further drilling in processor 90 andsends suitable drill control signals downhole by way of controllercircuit 92 and telemetry 74 to a downhole controller 94 for the drillmotor 14.

As illustrated in FIG. 4, the powering electronics 56 for themotor/generator set 54 includes an uphole clock 98 which generates asquare wave clock signal 100, illustrated in FIG. 5(A), that drives anFET switching circuit 102 which is connected by way of respective lines58 and 60 to supply an alternating current 104, illustrated in FIG.5(B), to the loops 26 and 28. Electronics 56 also includes meters 106for measuring the current in each loop.

The first step for processing the recorded magnetic field data atprocessor 90 is the generation of a reference wave form by a referenceclock 110 (FIG. 3) which is time synchronized with the clock 98 for theloop switching circuitry 102. Magnetic field data signals from thedownhole magnetometers 60 that are stored in the AC field data files 86are time averaged with respect to the reference wave form to produce twosingle-row data matrices of the three magnetic field components. This isdone for magnetic field signals generated by the magnetometers inresponse to the magnetic fields H1 and H2 produced by the loops 26 and28, respectively, either simultaneously when the loops are energized bydifferent frequencies, or sequentially when they are energized by asingle frequency. The location of the magnetic field sensor 60 withrespect to the two loops, and thus the location of the drill withrespect to the proposed path of the borehole, and the direction ofdrilling, can be determined by mathematically optimizing the matchbetween measured and computed field components using mathematically wellknown methods, e.g. by using a least squares fitting method.

Since the least squares method, using Taylor series expansions tolinearize the fitting process, is so well suited to computerizedanalysis of these data a procedure based upon this method will bedescribed. The first step is to precisely lay out the twoelectromagnetic source loops, or coils, 26 and 28 on the ground as shownin FIG. 6 for loop 26. As illustrated, the loop is defined by n straightline segments 120, which may be referred to generally as segments Ws(1). . . Ws(n), with adjacent segments being joined at nodes 122 The loop,or coil, 26 has N turns, and when energized by the source 56 carries anelectric current I. In the illustration, the positive current flowscounterclockwise. A surveyor's wire file listing the three dimensionalcoordinates of the vectors Rw(i), Rw(i−1) . . . Rw(i−n) with respect toa reference origin point 124 for the wire element nodes 122 of the coils26 and 28 is generated using standard land surveying techniques withcustomary away, elevation, right (aer) coordinate axes as illustrated inFIG. 6. Each node vector is defined by a vector Rw(i) from the origin124 by its away, elevation and right (aer) coordinates. The elevationunit vector e defining the aer system points vertically upwards, asillustrated by axis 130. The away axis 132 is horizontal, usually chosento be from the entry point toward the proposed borehole exit point, andthe right unit vector axis 134 is also horizontal and points to theright of the away axis.

The electromagnetic Law of Biot Savart can be used to compute the H1aerand H2aer (away, elevation, right) vector components of theelectromagnetic fields H1 and H2 specified in the away, elevation, rightcoordinate system for any location P at which the target electromagneticfield is to be evaluated. The location P is defined by the vector Raeras shown in FIG. 7. This is done by breaking each loop into an ensembleof wire segments such as segment Ws(i) shown in FIG. 7. The fieldgenerated by the current I carried in each of the N wires of eachsegment is readily found by summing vectorally the expressions for H(i)generated by each of the n wire segments Ws(i) shown in FIG. 6 for allthe wire segments constituting a loop.

The field H(i) for a wire segment as shown in FIG. 7, using “MATLAB”notation conventions in the following expressions, is:

H(i)=(N*I*Huv(i)/(4*pi*b))*(cos B(i)−cos A(i))

Huv=cross(Ws(i),r(i))/mag(cross(Ws(i),r(i))

b=mag(cross(Ws(i),r(i))

cos B(i)=dot(r(i),Ws(i))/(mag(r(i))*mag(Ws(i)))

cos A(i)=dot(r(i−1),Ws(i))/(mag(r(i−1))*mag(Ws(i)))  (Eq. 1)

The function mag denotes the conventional magnitude of a vector, e.g.mag(R) denotes sqrt(dot(R,R)). Thus the theoretical vectors H1aerth andH2aerth for the electromagnetic field vectors H1 and H2 generated byeach loop, as represented by their aer vector components, is readilydone.

To control the drilling of a borehole, the driller is given the proposedborehole path coordinates expressed in the aer coordinate system and themeasured borehole coordinates found in the course of drilling areexpressed in the same aer system. Usually, the coordinates of a boreholebeing drilled are obtained in the course of drilling using conventionalborehole surveying techniques based upon integrating a large number ofstation measurements of gravity and of the Earth's magnetic field alongthe borehole. The difficulty is that, far away from the borehole entrypoint, a borehole survey generated in this way does not have sufficientprecision due to the cumulative build up of error along the boreholelength. In accordance with the present invention, the driller isprovided with the approximate survey file of the borehole, and this isimproved upon using the method and apparatus of this invention.

To make an electromagnetic determination of the location and drillingazimuth, measurements of three components of the electromagnetic fieldsgenerated by the loops 26 and 28, and of gravity, are made by theborehole instrument 36 at a location P at a chosen depth, or awaydistance along the borehole. The instrument 36 sensing axes are definedby an xyz coordinate system 140 fixed to the downhole drilling tool. Thez axis 142 of system 140, illustrated in FIG. 8, is along the axis ofthe borehole, with the positive z axis pointing in the direction ofdrilling. The x and y axes 144 and 146, respectively, are perpendicularto z and to each other, the xyz system forms a right handed system ofcoordinate axes.

The analysis of the H1xyz and H2xyz data, i.e., the xyz vectorcomponents of the measurements of the down-hole electromagnetic fieldsproduced by loops 26 and 28, respectively, is best analyzed bytransforming them to a bes coordinate system 150, whose axes are shownin FIG. 9, and are shown together with those of the xyz system 140 inFIG. 8. The “b” axis of the bes system is the projection of the boreholedrilling direction on to the horizontal plane. The “e” direction isvertically upwards, i.e., the direction “e” of the “bes” coordinate axesis the same as “e” direction of the surveyors “aer” system. Thedirection “s” is in the horizontal plane and points to the right of theborehole. These directions are defined by the accelerometermeasurements. The direction of s is given by the vector cross product ofthe measured gravity vector g, g=[gx; gy; gz] and z, i.e., [0; 0; 1];the unit vector s is found by taking this cross product and dividing bythe magnitude of this vector, thus:

s=cross(g,z)/mag(cross(g,z))  (Eq. 2)

The elevation unit vector “e” is a unit vector pointing in the oppositedirection as g, i.e.

e=−g/mag(g)  (Eq. 3)

Finally, the projection of the borehole direction z in the horizontalplane is in the direction of the unit vector b given by

b=cross(e,s)  (Eq. 4)

The matrix to transform a vector represented by its xyz components toits representation using bes components is given by the 3 by 3 matrix:

xyztobes=[b′;e′;s′]  (Eq. 5)

The measurements of the electromagnetic fields H1x, H1y, H1z generatedby loop 1 are conveniently represented by the 3 by 1 matrix:

H1xyz=[H1x;H1y;H1z]  (Eq. 6)

Similarly, the measurements H2x, H2y, H2z are represented by the 3 by 1matrix:

H2xyz=[H2;H2y;H2z]  (Eq. 7)

And the representation of the H1 and H2 measurements in the bescoordinate system is given by the matrix products:

H1bes=xyztobes*H1xyz and H2bes=xyztobes*H2xyz  (Eq. 8)

These 3 by 1 matrix representations of the measurements of H1 and H2 areto be compared to theoretical values of the corresponding quantitiesH1th and H2th, which are conveniently calculated using the Law of BiotSavart with respect to the “aer” coordinate system used by the landsurveyor. The matrix representation of H1th and H2th with respect to theaer coordinate axes will be written as:

H1aerth=[H1ath;H1eth;H1rth] and

H2aerth=[H2ath,H2eth,H2rth]  (Eq. 9)

To compare the theoretical and measured field values, represent the H1thand H2th vectors in the bes coordinate system. The matrix to transformvectors from the aer system to the bes system is given by:

aertobes=[cos(Aab)0 sin(Aab);0 1 0;−sin(Aab)0 cos(Aab)]  (Eq. 10)

The representation of the theoretical values H1th and H2th calculatedwith respect to a surface aer system can be converted to a down-hole bessystem by the expressions:

H1besth=aertobes*H1aerth H2besth=aertobes*H2aerth  (Eq. 11)

The mathematical problem is thus reduced to finding the value of thevector R from the reference origin to the drill bit represented by the 3by 1 matrix Raer and of the azimuthal angle Aab (FIG. 9) between theaway axis and the horizontal projection of the drilling direction. Thus,four numbers are to be determined to give the best fit of H1besth andH2besth to the 6 measurements of the H1bes and H2bes. To do this, startwith an approximate value of R which is called Raer0, and an approximatevalue of the drilling azimuth which is called Aab0, and then form fromthem a 4 by 1 matrix RA0 i.e.:

RA0=[Ra0;Re0;Rr0;Aab0]  (Eq. 11)

The values of the elements of RA0 can usually obtained from thedriller's borehole survey, but if a survey is not available, an educatedguess is usually sufficient. Then, together with RA0, define anassociated 4 by 1 difference matrix:

dRA=[dRa;dRe;dRe,dAab]  (Eq. 12)

The intent is to make the elements of

RA=RA0+dRA  (Eq. 13)

such that the 6 values of H1besth and H2besth evaluated at the 4 elementvalues of RA match the 6 electromagnetic field measurement valuescontained in H1bes and H2bes. Call the values of H1besth and H2besth,evaluated at RA0, H1besth0 and H2besth0 and form a 6 by 1 matrixH12besth0, i.e.:

H12besth0=[H1bth0;H1eth0;H1sth0;H2bth0;H2eth0;H2sth0]  (Eq. 14)

The corresponding theoretically computed field values computed at RA,which at the moment is unknown, can be written as:

H12besth=[H1bth;H1eth;H1sth;H2bth;H2eth;H2sth]  (Eq. 15)

Now Taylor expand H12besth0 about the region RA0, and call that valueH12besth i.e. write the matrix equation which represents 6 linearequations with 4 unknowns, i.e.:

H12besth=H12besth0+dH12besdRAb*dRA.  (Eq. 16)

The quantity dH12besdRAb is a 6 by 4 matrix with 24 “derivative”elements, i.e.,

$\begin{matrix}{{{dH}\; 12{besdRAb}} = \begin{matrix}\left\lbrack {{dH}\; 1{bthdRa}} \right. & {{dH}\; 1{bthdRe}} & {{dH}\; 1{bthdRr}} & {{{dH}\; 1{bthdAab}};} \\{{dH}\; 1{ethdRa}} & {{dH}\; 1{bethdRe}} & {{dH}\; 1{ethdRr}} & {{{dH}\; 1{bthdAab}};} \\{{dH}\; 1{sthdRa}} & {{dH}\; 1{eshdRe}} & {{dH}\; 1{sthdRr}} & {{{dH}\; 1{bthdAab}};} \\{{dH}\; 2{bthdRa}} & {{dH}\; 12{bthdRe}} & {{dH}\; 2{bthdRr}} & {{{dH}\; 2{bthdAab}};} \\{{dH}\; 2{ethdRa}} & {{dH}\; 2{ethdRe}} & {{dH}\; 2{ethdRr}} & {{{dH}\; 2{ethdAab}};} \\{{dH}\; 2{sthdRa}} & {{dH}\; 2{sthdRe}} & {{dH}\; 2{sthdRr}} & \left. {{dH}\; 2{shdAab}} \right\rbrack\end{matrix}} & \left( {{Eq}.\mspace{14mu} 17} \right)\end{matrix}$

Each of the derivatives in this relation are to be read as calculuspartial derivatives evaluated at the element values contained in RA0;e.g., dH1bthdRa in the notation of calculus would be written asdH1bth/dRa. The derivative dH1bthdRa is the change in H1bth per unitchange in the parameter Ra near the RA0 while holding Re0, Rr0 and Aab0constant. In a computer program it can be computed, for example byevaluating H1bth at [Ra0; Re0; Rr0; Aab0] and at [Ra0+0.01; Re0; Rr0;Aab0] (where “0.01” is any appropriately small number). The first valueH1bth is subtracted from the second and this difference is divided by0.01, following the basic definition of differentiation.

To proceed, equate the Taylor series expansion (Eq.16) of H12besth aboutthe 4 by 1 matrix RA0 to the measurement matrix H12besmeas:

H12besmeas=H12besth=H12besth0+dH12besdRA*dRA

H12besmeas=[H1bes;H2bes]  (Eq. 18)

This over determined equation is readily solved for dRA in the leastsquares sense using the computer program “MATLAB” operation of leftmatrix division as

dRA=dH12besdRA\(H12besmeas−H12besth0)  (Eq. 19)

The improved value for the 4 by 1 matrix RA, which contains the elementvalues wanted is:

RA=RA0+dRA  (Eq. 20)

This procedure is repeated iteratively using this value of RA for a newRA0. The procedure quickly minimizes the quantity Error2 given by theinner matrix product below of the last iteration; i.e.:

Error2=(H12bes−H12besth)′*(H12bes−H12besth)  (Eq. 21)

Thus the value of the drill bit location Raer and the azimuthal drillingdirection with respect to the a axis; i.e., the angle Aab, have beendetermined from electromagnetic and accelerometer measurements.

Alternatively, the location vector Raer to the drilling point can bedetermined from the measured vectors H1xyz and H2xyz without the use ofan accelerometer. This can be done by comparing scalar vector invariantsof the measured electromagnetic field vectors to corresponding computedvalues. To demonstrate this method, consider the magnitude of H1, themagnitude of H2 and the magnitude of the projection of (H1−H2) upon aplane perpendicular to (H1+H2). The approximate inverse cube decrease inthe field magnitudes H1 and H2 with the distance away from each sourceloop makes these quantities good for determining the away component Raand the right side component Rr. For two similar laterally separatedloops lying on approximately the same plane the H1 and H2 vectors arevertical at the Earth's surface; however, the direction of these vectorsdiverge direction with depth into the Earth. Thus the projection of thedifference vector H1−H2 onto the plane perpendicular to the direction ofH1+H2; i.e., the near vertical direction, can give a good measure of theelevation component Re. These three parameters are not only good forthis idealized configuration but also for most cases of practicalinterest.

Thus, the three quantities H1mag, H2mag and H12mag, defined below, canbe computed from the H1 and H2 measurements and from theoreticalcomputations; i.e.:

H1mag=sqrt(dot(H1,H1))

H2mag=sqrt(dot(H2,H2))

H12mag=sqrt(dot(H12p,H12p)

H12p=(H1−H2)−dot((H1−H2),H12plusuv)*H12plusuv

H12plus=H1+H2

H12plusuv=H12plus/sqrt(dot(H12plus,H12plus))  (Eq. 22)

From the three quantities H1mag, H2mag and H12mag, form the 3 by 1 fieldmeasurement matrix H12perpmeas; i.e.:

H12perpmeas=[H1mag;H2mag;H12mag];  (Eq. 23)

A first guess for the aer representation of the sensor location vectorRaer0 is written as a 3 by 1 matrix, as follows:

Raer0=[Ra0;Re0;Rr0];  (Eq. 24)

The vector Raer to the best fit sensor location is written asRaer0 plusa small correction 3 by 1 correction matrix dRaer; i.e.:

Raer=Raer0+dRaer=Raer0+[dRa;dRe; dRr];  (Eq. 25)

Using the same procedure as defined by FIG. 7 and (Eq.1), compute H1th0and H2th0 at the presumed location Raer0. Then compute theoreticalvalues of the matrix elements of H12perpth0; i.e., the theoreticalmatrix following the steps in (Eq.23), To evaluate the matrix H12perpthat the true value of Raer, use a Taylor series approach using aderivative matrix dH12perpdRaer; i.e.:

H12perpth=H12perpth0+dH12perpdRaerdRaer  (Eq. 26)

The derivative matrix dH12perpdRaer is similar to the derivative matrixof (Eq.17); i.e.

$\begin{matrix}{\; {{{dH}\; 12{perpdRaer}} = \begin{matrix}\left\lbrack {{dH}\; 1{magdRa}} \right. & {{dH}\; 1{magdRe}} & {{{dH}\; 1{magdRr}};} \\{{dH}\; 2{magdRa}} & {{dH}\; 2{magdRe}} & {{{dH}\; 2{magdRr}};} \\{{dH}\; 12{magdRa}} & {{dH}\; 12{magdRe}} & \left. {{{dH}\; 12{magdRr}};} \right\rbrack\end{matrix}}} & \left( {{Eq}.\mspace{14mu} 27} \right)\end{matrix}$

As in (Eq. 17), each of the elements of dH12perpdRaer is a partialderivative; e.g., dH1magdRa is the partial derivative of H1mag withrespect to Ra, etc., and can be computed in the same manner as outlinedfor the elements of the matrix of (Eq. 17). The three linear equationsimplicit in (Eq. 26) are solved for the three unknowns in dRaer, afterequating H12perpth to the corresponding 3 by 1 measurement matrixH12perpmeas The solution for dRaer is found using the MATLAB “\”operation, as:

dRaer=dH12perpdRaer\(H12perpmeas−H12perpth0)  (Eq. 28)

The improved value for the 3 by 1 matrix Raer is:

Raer=Raer0+dRaer  (Eq. 29)

This procedure is repeated iteratively using this value of Raer for anew Raer0 to minimize the error implicit with the linear nature of aTaylor expansion. The final Raer matrix has the three components of thedrill bit location vector Raer required to locate the drill bit withrespect to the proposed path. From this, the driller can determine theappropriate drill control signals needed to progress along the path tothe desired exit point.

Although the present invention has been described in terms of apreferred embodiment, it will be understood that variations andmodifications may be made in the above-described system withoutdeparting from the true spirit and scope thereof as defined in thefollowing claims.

1. A method for drill guidance, comprising: determining a proposed pathfor a borehole; positioning first and second current-conducting loops inknown, laterally separated locations with respect to said proposed path;causing said first and second loops to generate corresponding first andsecond magnetic fields, each of said fields having an alternatingpolarity; positioning magnetic field sensors at a measurement locationin said borehole; measuring, at said measurement location, the vectorcomponents of said first and second magnetic fields and determining,from said measured vector components of said first and second fields,the location of the sensors with respect to the locations of themagnetic loop sources.
 2. The method of claim 1, further including:determining the direction of the gravity vector at said measurementlocation; and determining from said gravity vector and said measuredmagnetic field vectors the direction of the borehole at said sensorswith respect to a surface direction.
 3. The method of claim 1, whereingenerating electromagnetic fields includes directing alternatingcurrents of known amplitude and frequency through said loops.
 4. Themethod of claim 1, wherein generating electromagnetic fields includessimultaneously directing alternating currents of known amplitudes anddifferent frequencies through each of said loops.
 5. The method of claim1, wherein positioning said first and second loops includes placing saidloops on opposite sides of said proposed path.
 6. The method of claim 1,further including determining the lateral distance of said measuringlocation from the proposed path and the direction of said borehole withrespect to the direction of the proposed path.
 7. Apparatus for boreholesurveys comprising: a downhole tool located in a borehole in the Earth,said tool having an axis and including a magnetometer for measuring x, yand z vector components of magnetic fields at the tool; anelectromagnetic excitation system including two electrical loopconductors at known locations, laterally spaced from each other and froma proposed path of said borehole, and carrying known alternatingelectrical currents producing corresponding alternating electromagneticfields in the region of said magnetometer; computer circuitry; atelemetry link for transmitting measurement data signals correspondingto the respective measured vectors of magnetic fields generated by eachof said loops from said magnetometer to said computer circuitry; andcircuits in said computer circuitry responsive to said measurementsignals for determining the location of the borehole sensors.
 8. Theapparatus of claim 7, wherein said downhole tool further includessensors for measuring the Earth's gravity vector and for determining theorientation of the downhole tool, said telemetry link transmittingmeasurement data signals corresponding to said gravity vector andorientation measurement to said computer for determination of thedirection of the borehole with respect to said proposed path.
 9. Theapparatus of claim 8, wherein said downhole tool is a measurement whiledrilling instrument.
 10. The apparatus of claim 8, wherein theelectrical current supplied to each of said loops is an alternatingcurrent of a different frequency.
 11. The apparatus of claim 8, wherein:said two electrical loop conductors carry first and second alternatingcurrents, respectively, said currents producing corresponding first andsecond electromagnetic fields in the region of said downhole tool insaid borehole; and said electrical loop conductors are spaced onopposite sides of said proposed path of said borehole.
 12. The apparatusof claim 11, wherein each of said loop conductors comprises multipleturns of wire.
 13. A method for location determination, comprising:positioning first and second current-conducting loops at known spacedlocations; energizing said loops with known electrical currents toproduce corresponding first and second electromagnetic fields;positioning a magnetic field vector sensor to detect x, y and z vectorcomponents of said first and second fields; and determining from saidvector components the location of said sensor with respect to saidloops.
 14. The method of claim 13, wherein: positioning said loopsincludes positioning the loops on opposite sides of a proposed path tobe followed by said sensor; and determining the location of said sensorincludes locating said sensor with respect to said path.
 15. The methodof claim 13, wherein energizing said loops includes supplyingalternating current of a known amplitude and frequency to one loop at atime.
 16. The method of claim 13, wherein energizing said loops includessupplying alternating current of known amplitude and different knownfrequencies to each loop.
 17. The method of claim 13, further including:detecting, at the location of said sensor, the Earth's gravity vectorsand the orientation vectors of the sensor; and determining from saidvectors the direction of the sensor with respect to the locations ofsaid loops.
 18. The method of claim 13, wherein determining the locationof the sensor includes: time averaging magnetic field vector dataobtained for each of said loops by the sensor; calculating theoreticallocation vectors for the sensor; and optimizing the match betweentheoretical location values and measured magnetic field vector data todetermine the location of the sensor.
 19. The method of claim 18,wherein; positioning said loops includes positioning the loops onopposite sides of a proposed path to be followed by said sensor; anddetermining the location of said sensor includes locating said sensorwith respect to said path.
 20. The method of claim 19, whereinenergizing said loops includes supplying alternating current of a knownamplitude and frequency to one loop at a time.
 21. The method of claim19, wherein energizing said loops includes supplying alternating currentof known amplitude and different known frequencies to each loop.